A plane flies faster so you can amortize the cost over more flights. A plane only requires 2 airports, which can be used as a starting point to connect with any other airport again amortizing the cost over many flights. For trains you need rail all the way, which is not flexible and costs a lot.

Then the planes don't pay their full cost as they emit a lot of CO2 but aviation fuel is not taxed so you get planes that already have quite a lot of structural advantages getting even cheaper.

Budget airlines are probably also run a lot more efficiently than most train systems